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Romashka-Z-Leto [24]
3 years ago
6

If the coordinates of the endpoints of a diameter of the circle are​ known, the equation of a circle can be found.​ First, find

the midpoint of the​ diameter, which is the center of the circle. Then find the​ radius, which is the distance from the center to either endpoint of the diameter. Finally use the​ center-radius form to find the equation.
Mathematics
1 answer:
Evgesh-ka [11]3 years ago
4 0

Answer:

The equation of the circle is (x+3)^2+(y-5)^2 = 17

Step-by-step explanation:

The complete question is

If the coordinates of the endpoints of a diameter of the circle are​ known, the equation of a circle can be found.​ First, find the midpoint of the​ diameter, which is the center of the circle. Then find the​ radius, which is the distance from the center to either endpoint of the diameter. Finally use the​ center-radius form to find the equation.

Find the center-radius  form of the circle having the points (1,4) and (-7,6) as the endpoints of a diameter.

Consider that, if both points are the endpoints of a diameter, the center of the circle is the point that is exactly in the middle of the two points (that is, the point whose distance to each point is equal). Given points (a,b) and (c,d), by using the distance formula, you can check that the middle point is the average of the coordinates. Hence, the center of the circle is given by

(\frac{1-7}{2}, \frac{4+6}{2}) = (-3,5).

We will find the radius. Recall that the radius of the circle is the distance from one point of the circle to the center. Recall that the distance between points (a,b) and (c,d) is given by \sqrt[]{(a-c)^2+(b-d)^2}. So, let us use (1,4) to calculate the radius.

r = \sqrt[]{(1-(-3))^2+(4-5)^2} = \sqrt[]{17}.

REcall that given a point (x_0,y_0). The equation of a circle centered at the point (x_0,y_0) is

(x-x_0)^2+(y-y_0)^2 = r^2

In our case, (x_0,y_0)=(-3,5) and r=\sqrt[]{17}. Then, the equation is

(x-(-3))^2+(y-5)^2 = (x+3)^2+(y-5)^2 = 17

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Step-by-step explanation:

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balu736 [363]

Answer:

2.

a)1

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Step-by-step explanation:

There's some identity trigonometric equation, which are valid for all angles,and they doesn't depends on the measure of angle!

some of em are follows:. (x is the given angle)

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You can remember these identity, its gonna help alot.

now back to question,. {x is representing angles)

for (a) sin(x)^2+cos(x)^2=1, this is true for all x, dat means that for all the angle given in question(for ,15°,30°,45°,60° and 120°),we will get 1

for(b) ,

cosec(x)^2=1+cot(x)^2

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sec(x)^2=1+tan(x)^2

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In a sample of students, 125 said they exercise on a regular basis. How large was the sample if 27.3% said they exercised on a r
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First, let's declare a variable

x = # of students

Now, let's create an equation to model the problem.

x * 0.273 = 125

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marin [14]

Answer:

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Step-by-step explanation:

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hope this helps :)

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